JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

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Analyzing +4 | -1

f(x)=\left\{\begin{array}{cc}x e^{\left(-\frac{1}{|x|}+\frac{1}{x}\right)}, & x \neq 0 \\ 0, & x=0\end{array}\right.

then

f(x)

View answer and explanation

Correct option: C

continuous for all

x

but not differentiable at

x=0

Option C (continuous for all

x

but not differentiable at

x=0

) is correct because the function is continuous at

x=0

after evaluating the limits, but the left-hand derivative and right-hand derivative at

x=0

are not equal.

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